The name Baxter is a boy's name of English origin meaning "baker". Baxter and is often added to lists like English Names for Boys and discussed in our forums with posts like "Boys Makeover- Two Middles".
From the experts:
An x makes any name cooler, so that Baxter has a bit more pizzazz than the original Baker. Baxter had some currency as a first name a century ago--it was on the popularity lists sporadically from 1880 till the 1920s, peaking at Number 515 in 1886-- which means it's just about due for a comeback. And we can see Bax as a worthy follow-up to Max and Jax.
Singer Ian Dury named his now-grown son Baxter, and Dr. Baxter Stockman was a scientist in the "Teenage Mutant Ninja Turtle" series.